Question

A person is running on a horizontal circular track of radius R. In the first round, he runs with speed v and takes time t. If he takes time 2t covering the same track in the second round, then his speed will be
(i) $\frac{v}{2}$
(ii) 2v
(iii) $\frac{\pi R}{t}$
(iv) $\frac{\pi R}{t}$

• A. (ii) and (iii)
• B. (i) and (iii)
• C. (i) and (iv)
• D. (ii) and (iv)

Answer 1

The correct option is B (i) and (iii)

For first round:
Radius of circular track = R
Time taken by the person to complete the first round = t
Speed, $v=\frac{\text{Distance covered}}{\text{Time taken}}$
Distance covered by the person, s = circumference of circular track = 2πR
$\Rightarrow v=\frac{2\pi R}{t}$
For second round:
Let the new speed of the person be v′.
Distance, s = 2πR
Time, $t^{\prime }=2t$
$\Rightarrow v^{\prime }=\frac{s}{t^{\prime }}$
$\Rightarrow v^{\prime }=\frac{2\pi R}{t}$
$\Rightarrow v^{\prime }=\frac{1}{2}\left(\frac{2\pi R}{t}\right)=\frac{\pi R}{t}$
$\Rightarrow v^{\prime }=\frac{v}{2}$ $(\because v=\frac{2\pi R}{t})$
Hence, the correct answer is option (b).